17.
\(sinx\ne-1\Leftrightarrow x\ne\dfrac{3\pi}{2}+k2\pi\)
19.
\(cos\left(2x-\dfrac{\pi}{3}\right)\ne0\Leftrightarrow2x-\dfrac{\pi}{3}\ne\dfrac{\pi}{2}+k\pi\Leftrightarrow x\ne\dfrac{5\pi}{12}+\dfrac{k\pi}{2}\)
21.
\(sin2x\in\left[-1;1\right]\Rightarrow y=3sin2x-5\in\left[-8;-2\right]\Rightarrow\left\{{}\begin{matrix}y_{min}=-8\\y_{max}=-2\end{matrix}\right.\)
22.
\(cos\left(x+\dfrac{\pi}{4}\right)\in\left[-1;1\right]\Rightarrow y=7-2cos\left(x+\dfrac{\pi}{4}\right)\in\left[5;9\right]\Rightarrow\left\{{}\begin{matrix}y_{min}=5\\y_{max}=9\end{matrix}\right.\)
23.
Hàm số xác định khi: \(1-cosx\ne0\Leftrightarrow cosx\ne1\Leftrightarrow x\ne k2\pi\).
20.
Hàm số xác định khi: \(\left\{{}\begin{matrix}cosx\ne0\\sinx\ne0\end{matrix}\right.\Leftrightarrow x\ne\dfrac{k\pi}{2}\).
24.
Hàm số xác định khi:
\(sinx-cosx\ne0\Leftrightarrow sin\left(x-\dfrac{\pi}{4}\right)\ne0\Leftrightarrow x-\dfrac{\pi}{4}\ne k\pi\Leftrightarrow x\ne\dfrac{\pi}{4}+k\pi\).
25.
ĐK: \(x\in R\)
\(sinx\in\left[-1;1\right]\Rightarrow y=4\sqrt{sinx+3}-1\in\left[4\sqrt{2}-1;7\right]\Rightarrow\left\{{}\begin{matrix}y_{min}=4\sqrt{2}-1\\y_{max}=7\end{matrix}\right.\)
